QQuestionMathematics
QuestionMathematics
EXERCISE 7.4.1: Find the connected components of each graph.
(a) Graph G = (V, E)
V = {a, b, c, d, e, f, g, h, i, j}
E = {{f, h}, {e, d}, {c, b}, {i, j}, {a, b}, {i, f}, {f, j}}
(b) Graph G = (V, E)
V = {a, b, c, d, e}
E = ∅
(c) Graph G = (V, E)
V = {a, b, c, d, e, f}
E = {{c, f}, {a, b}, {d, a}, {e, c}, {b, f}}
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Answer
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Step 1I'll solve this graph theory problem step by step, focusing on finding the connected components for each graph.
(a) Graph G = (V, E)
Step 2: Identify Connections
\begin{array}{l}
- Create an adjacency list to track connections: a: \{b\} \ b: \{a, c\} \ c: \{b\} \ d: \{e\} \ e: \{d\} \ f: \{h, i, j\} \ h: \{f\} \ i: \{f, j\} \ j: \{i, f\} \end{array}
Final Answer
(b) Graph G = (V, E) Step 1: Analyze Graph - No edges exist - Each vertex is isolated (c) Graph G = (V, E) Step 1: Create Adjacency List \begin{array}{l} a: \{b, d\} \ b: \{a, f\} \ c: \{e, f\} \ d: \{a\} \ e: \{c\} \ f: \{b, c\} \end{array} Step 2: Trace Connections - All vertices are connected through various paths - Single connected component
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